A novel methodology is presented in this paper for the workspace analysis of virtual axis machine tools. The workspace is defined which enables to describe in a unified framework both the position and orientation capabilities of the mobile platform. Given a range of the orientation of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary in fact is the cap of twelve envelope surfaces. Two examples are given to illustrate the effectiveness of this approach.

1.
Cleary, K. and Arai, T., 1991, “A Prototype Parallel Manipulator: Kinematics, Construction, Software, Workspace Results, and Singularity Analysis,” IEEE Proc. on Robotics and Automation, pp. 566–571.
2.
Fichter
E. F.
,
1986
, “
A Stewart Platform-Based Manipulator: General Theory and Practical Construction
,”
Int. J. of Robotics Research
, Vol.
5
, No.
2
, pp.
157
182
.
3.
Eisenhart, L. P., 1960, A Treatise on the Differential Geometry of Curves and Surfaces, Dover Publications, Inc., New York.
4.
Huang, T., Wang, J. S., and Whitehouse, D. J., 1997, “An Effective Algorithm for Workspace Evaluation of Virtual Axis Machine Tools,” Proc. of Int. Conf. on Mechanisms and Machinery Transmission, China.
5.
Huang
T.
,
Whitehouse
D. J.
, and
Wang
J. S.
,
1998
, “
Local Dexterity, Optimal Architecture and Design Criteria of Parallel Machine Tools
,”
CIRP Annals
, Vol.
47
, No.
1
, pp.
347
351
.
6.
Huang, T., Wang, J. S., Gosselin, C., and Whitehouse, D. J., “Determination of Closed Form Solution to the Orientation Workspace of Stewart Parallel Manipulators,” submitted to IEEE Trans. on Robotics and Automation.
7.
Gosselin
G.
,
1990
, “
Determination of the Workspace of 6-DOF Parallel Manipulators
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
11
, No.
3
, pp.
331
336
.
8.
Ji
Z.
,
1994
, “
Workspace Analysis of Stewart Platforms via Vertex Space
,”
J. of Robotic Systems
, Vol.
11
, No.
7
, pp.
631
638
.
9.
Jo
D. Y.
,
1989
, “
Workspace Analysis of Closed Loop Mechanisms with Unilateral Constraints
,”
ASME Des. Eng. Div. Publication, Advance in Design Automation
, Vol.
3
pp.
53
60
.
10.
Kim, D. I., Ching, W. K., and Youm, Y., 1997, “Geometrical Approach for the Workspace of 6DOF Parallel Manipulators,” IEEE Int. Conf. on Robotic and Automation, pp. 2986–2991.
11.
Kumar
V.
,
1992
, “
Characterization of Workspaces of Parallel Manipulators
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
114
, No.
3
, pp.
368
375
.
12.
Luh
C. M.
, et al.,
1996
, “
Working Capability Analysis of Stewart Platform
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
118
, No.
2
, pp.
221
227
.
13.
Merlet, J. P., 1987, “Parallel Manipulators, Part I: Theory, Design Kinematics, Dynamics and Control,” Technical Report No. 646 INRIA, France.
14.
Merlet, J. P., 1992, “Geometrical Determination of Workspace of a Constrained Parallel Manipulators,” in ARK, France, pp. 326–329.
15.
Merlet
J. P.
,
1995
, “
Determination of the Orientation Workspace of Parallel Manipulators
,”
J. of Intelligent and Robotic Systems
, Vol.
13
, pp.
143
160
.
16.
Stewart
D.
,
1965
, “
A Platform with 6 Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
, Vol.
180
, No.
15
, pp.
371
386
.
17.
Stoughton
R. S.
, and
Arai
T.
,
1993
, “
A Modified Stewart Platform Manipulator with Improved Dexterity
,”
IEEE Trans, on Robotics and Automation
, Vol.
9
, No.
2
, pp.
166
173
.
18.
Tosatti
L. M.
, et al.,
1998
, “
An Integrated Method for the Design of Parallel Kinematics Machines (PKM)
,”
CIRP Annals
, Vol.
47
, No.
1
, pp.
341
345
.
19.
Yang
D. C. H.
, and
Lee
T. W.
,
1984
, “
Feasibility Study of a Platform Type Robotic Manipulators from a Kinematic Viewpoint
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, No.
2
, pp.
191
198
.
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